Background

This analysis document compliments FIA - NLS Models: Biomass Growth vs. Stand Age. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different growth estimators.

Here, we fit the models using: 1) calculated plot biomass growth (Mass-Balance method) using only trees >5 inches (12.5 cm) dbh (\(G_{MassBal > 5}\)), and 2) plot biomass growth (tree incremental growth method) for trees >5 inches (12.5 cm) dbh (\(G_{TI-NoIngrow}\)).

Below the model fitting procedure is implemented by ecoprovince:

Analysis 1: \(G_{MassBal > 5}\)

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6869     3003.0                                
## 2   6868     2999.0  1   4.02  9.2031  0.002425 ** 
## 3   6816     2317.2 52 681.73 38.5625 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 29089.03
## 2     2 29081.82
## 3     3 27199.38
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.135803   0.268134   4.236 2.31e-05 ***
## phi    0.014255   0.005449   2.616  0.00891 ** 
## alpha  0.183105   0.039688   4.614 4.03e-06 ***
## a      0.540533   0.168453   3.209  0.00134 ** 
## b      2.206353   0.192853  11.441  < 2e-16 ***
## c     52.447690   0.985862  53.200  < 2e-16 ***
## d      1.318388   0.086649  15.215  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5831 on 6816 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (54 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  19351    10991.7                                 
## 2  19346    10966.6   5   25.2  8.8747 1.989e-08 ***
## 3  18857     6831.3 489 4135.3 23.3433 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 82798.28
## 2     2 82741.70
## 3     3 72658.31
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.567865   0.223569   7.013 2.41e-12 ***
## phi    0.025003   0.003714   6.733 1.71e-11 ***
## alpha  0.184180   0.028101   6.554 5.74e-11 ***
## a      0.356236   0.022152  16.081  < 2e-16 ***
## b      1.777209   0.061579  28.860  < 2e-16 ***
## c     41.469035   0.427180  97.076  < 2e-16 ***
## d      1.238169   0.022233  55.691  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6019 on 18857 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3851 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 45 rows containing missing values (geom_point).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7319     3321.1                                
## 2   7318     3312.6  1   8.51  18.803 1.469e-05 ***
## 3   7254     2924.1 64 388.52  15.060 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 33832.56
## 2     2 33815.76
## 3     3 32720.09
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.74789    0.14029  -5.331 1.01e-07 ***
## phi    0.01983    0.00557   3.560 0.000374 ***
## alpha  0.54471    0.04161  13.090  < 2e-16 ***
## a      1.25134    0.46881   2.669 0.007620 ** 
## b      3.37115    0.47544   7.091 1.46e-12 ***
## c     46.48696    1.94765  23.868  < 2e-16 ***
## d      1.76805    0.21005   8.417  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6349 on 7254 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (72 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value  Pr(>F)    
## 1   5044     2546.6                                
## 2   5043     2543.9   1    2.66  5.2805 0.02161 *  
## 3   4823     1161.8 220 1382.14 26.0813 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25129.16
## 2     2 25125.88
## 3     3 20632.07
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.13139    0.25293  -0.519  0.60345    
## phi    0.03017    0.01011   2.984  0.00286 ** 
## alpha  0.40476    0.05142   7.872 4.27e-15 ***
## a      0.78330    0.11551   6.781 1.33e-11 ***
## b      2.69267    0.15975  16.856  < 2e-16 ***
## c     52.54274    1.61992  32.435  < 2e-16 ***
## d      1.34553    0.07458  18.041  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4908 on 4823 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1015 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Error in nls(fg2_MBg5, data = G_223, start = c(ge = ge.start, a = a.start,  : 
##   parameters without starting value in 'data': phi
##   model      AIC
## 1     1 40473.24
## 2     2       NA
## 3     3 36463.41
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.467315   0.144891  -3.225 0.001263 ** 
## phi    0.000000   0.006509   0.000 1.000000    
## alpha  0.375168   0.043377   8.649  < 2e-16 ***
## a      1.275827   0.341585   3.735 0.000189 ***
## b      2.573411   0.343780   7.486 7.81e-14 ***
## c     36.257429   1.192385  30.407  < 2e-16 ***
## d      1.480254   0.160021   9.250  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5338 on 8729 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1274 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  13446     8033.9                                  
## 2  13445     8027.2   1    6.66 11.1542 0.0008407 ***
## 3  13194     6846.6 251 1180.59  9.0641 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69488.49
## 2     2 69479.34
## 3     3 66707.05
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     2.066238   0.236245   8.746  < 2e-16 ***
## phi    0.013774   0.004729   2.913  0.00359 ** 
## alpha  0.601642   0.022273  27.012  < 2e-16 ***
## a      0.682610   0.091980   7.421 1.23e-13 ***
## b      3.572651   0.149622  23.878  < 2e-16 ***
## c     24.576045   0.336579  73.017  < 2e-16 ***
## d      1.540009   0.044687  34.462  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7204 on 13194 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (316 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 30 rows containing missing values (geom_point).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value    Pr(>F)    
## 1  13504     9840.7                                 
## 2  13503     9834.4   1   6.37  8.7513  0.003099 ** 
## 3  13220     9027.8 283 806.59  4.1737 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 69847.07
## 2     2 69840.31
## 3     3 67887.84
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.629451   0.242248   6.726 1.81e-11 ***
## phi    0.013328   0.005165   2.580  0.00988 ** 
## alpha  0.588401   0.022782  25.827  < 2e-16 ***
## a      0.545364   0.113742   4.795 1.65e-06 ***
## b      3.503712   0.168790  20.758  < 2e-16 ***
## c     23.685176   0.381675  62.056  < 2e-16 ***
## d      1.624809   0.055735  29.153  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8264 on 13220 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (402 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 66 rows containing missing values (geom_point).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   1368    1225.98                              
## 2   1367    1225.97  1   0.008  0.0092 0.9237    
## 3   1315     933.16 52 292.809  7.9351 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7586.402
## 2     2 7588.393
## 3     3 7031.294
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    1.634e+00  1.274e+00   1.283   0.1998    
## phi   3.623e-04  2.372e-02   0.015   0.9878    
## alpha 7.134e-01  9.118e-02   7.823 1.05e-14 ***
## a     1.732e+00  1.590e+00   1.089   0.2764    
## b     2.114e+00  1.596e+00   1.325   0.1854    
## c     2.603e+01  3.658e+00   7.115 1.83e-12 ***
## d     1.541e+00  9.306e-01   1.656   0.0979 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8424 on 1315 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (66 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits ### plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89838, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.0397, p-value = 4.663e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value Pr(>F)    
## 1   1888     947.45                              
## 2   1887     947.45   1   0.00   0.000      1    
## 3   1772     380.43 115 567.01  22.966 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9343.582
## 2     2 9345.582
## 3     3 7301.476
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.79937    0.56065   1.426  0.15411    
## phi    0.01272    0.01241   1.025  0.30529    
## alpha  0.05465    0.10935   0.500  0.61729    
## a      1.62452    0.35714   4.549 5.76e-06 ***
## b      0.97980    0.34828   2.813  0.00496 ** 
## c     40.36397    3.54417  11.389  < 2e-16 ***
## d      1.21487    0.37060   3.278  0.00107 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4633 on 1772 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (516 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.81073, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.8019, p-value = 6.099e-15
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    710    1183.68                                 
## 2    709    1169.58  1  14.093  8.5431  0.003579 ** 
## 3    666     945.02 43 224.565  3.6805 3.542e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3587.653
## 2     2 3581.089
## 3     3 3319.214
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.63859    1.25611   0.508 0.611350    
## phi    0.08964    0.03345   2.680 0.007544 ** 
## alpha  0.22908    0.22321   1.026 0.305122    
## a      1.01818    0.30866   3.299 0.001023 ** 
## b      1.98761    0.55333   3.592 0.000352 ***
## c     23.95708    2.37494  10.087  < 2e-16 ***
## d      0.85191    0.18245   4.669 3.66e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.191 on 666 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (44 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91339, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.1185, p-value = 3.08e-07
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6765     2158.6                                
## 2   6764     2155.4  1  3.189  10.008  0.001565 ** 
## 3   6740     2077.4 24 77.937  10.536 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25640.90
## 2     2 25632.89
## 3     3 25350.55
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     2.020678   0.339061   5.960 2.66e-09 ***
## phi    0.014575   0.004934   2.954  0.00315 ** 
## alpha  0.191226   0.035348   5.410 6.52e-08 ***
## a      0.278919   0.108523   2.570  0.01019 *  
## b      1.980364   0.146760  13.494  < 2e-16 ***
## c     58.303418   1.209829  48.191  < 2e-16 ***
## d      1.388516   0.073400  18.917  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5552 on 6740 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   8308     4415.0                             
## 2   8307     4415.0  1   0.00   0.000 0.9998    
## 3   8252     4106.1 55 308.95  11.289 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 40211.66
## 2     2 40213.66
## 3     3 39425.66
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.585873   0.212996   2.751  0.00596 ** 
## phi    0.000000   0.006393   0.000  1.00000    
## alpha  0.581593   0.056019  10.382  < 2e-16 ***
## a      1.342455   0.462513   2.903  0.00371 ** 
## b      2.784604   0.461040   6.040 1.61e-09 ***
## c     33.907419   1.305147  25.980  < 2e-16 ***
## d      1.550452   0.205951   7.528 5.68e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7054 on 8252 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (56 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    890     500.00                         
## 2    889     500.00  1 0.0000  0.0000 1.0000
## 3    882     494.01  7 5.9895  1.5277 0.1542
##   model      AIC
## 1     1 3721.381
## 2     2 3723.381
## 3     3 3699.880
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.47372    1.44590   1.711 0.087460 .  
## phi    0.00000    0.02552   0.000 1.000000    
## alpha  0.39600    0.16041   2.469 0.013751 *  
## a      1.54882    0.32376   4.784 2.01e-06 ***
## b      1.26860    0.36223   3.502 0.000485 ***
## c     29.68437    1.99852  14.853  < 2e-16 ***
## d      0.49984    0.10422   4.796 1.90e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7484 on 882 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94889, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1798, p-value = 0.001474
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1000     566.90                                
## 2    999     563.39  1  3.511  6.2249   0.01276 *  
## 3    986     515.05 13 48.343  7.1190 2.222e-13 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4308.841
## 2     2 4304.598
## 3     3 4182.594
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.34276    1.54565   1.516 0.129914    
## phi    0.04332    0.02507   1.728 0.084294 .  
## alpha  0.44951    0.11572   3.885 0.000109 ***
## a      0.00000    5.52454   0.000 1.000000    
## b      2.01907    5.51282   0.366 0.714258    
## c     26.31121    4.82682   5.451 6.33e-08 ***
## d      2.73767    4.45733   0.614 0.539229    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7227 on 986 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.94511, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.0956, p-value = 1.09e-09
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   3140     2796.3                             
## 2   3139     2796.0  1   0.32   0.359 0.5491    
## 3   3126     2660.4 13 135.63  12.259 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 17424.89
## 2     2 17426.53
## 3     3 17229.36
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.75073    0.27996  -6.253 4.56e-10 ***
## phi    0.03950    0.01826   2.164   0.0306 *  
## alpha  0.95397    0.07539  12.653  < 2e-16 ***
## a      6.71695    0.64071  10.484  < 2e-16 ***
## b      5.31578    0.99635   5.335 1.02e-07 ***
## c     34.74904    1.57550  22.056  < 2e-16 ***
## d      0.32758    0.05318   6.160 8.21e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9225 on 3126 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (91 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92891, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -14.071, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   1681     625.59                               
## 2   1680     587.31  1 38.279 109.4970 < 2e-16 ***
## 3   1667     579.35 13  7.957   1.7612 0.04396 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8778.340
## 2     2 8673.884
## 3     3 8607.333
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.00838    0.30608  -6.562 7.08e-11 ***
## phi    0.22025    0.01626  13.546  < 2e-16 ***
## alpha  0.51836    0.11645   4.451 9.09e-06 ***
## a      0.00000    9.48494   0.000    1.000    
## b      9.21284    9.45565   0.974    0.330    
## c     47.43124    8.60479   5.512 4.10e-08 ***
## d      2.78559    1.92378   1.448    0.148    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5895 on 1667 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (303 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89324, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.95054, p-value = 0.3418
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 9 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    360     160.54                             
## 2    359     159.32  1 1.22705  2.7650 0.09722 .
## 3    358     158.77  1 0.54375  1.2261 0.26892  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1023.403
## 2     2 1022.602
## 3     3 1023.355
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)    
## ge  -2.15379    0.40652  -5.298 2.05e-07 ***
## phi  0.05231    0.02682   1.951 0.051867 .  
## a    0.00000    5.22047   0.000 1.000000    
## b    3.39430    5.29020   0.642 0.521529    
## c   55.12209   16.07696   3.429 0.000677 ***
## d    1.96404    2.19982   0.893 0.372552    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6662 on 359 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.949, p-value = 6.568e-10
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.11276, p-value = 0.9102
## alternative hypothesis: two.sided

predict and plot

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1736     1481.0                                 
## 2   1735     1469.4  1  11.569  13.660 0.0002259 ***
## 3   1718     1335.2 17 134.204  10.157 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 5173.137
## 2     2 5161.484
## 3     3 4986.083
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.55586    0.66949  -0.830    0.406    
## phi    0.07262    0.01548   4.690 2.94e-06 ***
## alpha  0.51606    0.06292   8.202 4.59e-16 ***
## a      0.77418    0.18762   4.126 3.86e-05 ***
## b      1.22747    0.23917   5.132 3.19e-07 ***
## c     65.00451    4.28144  15.183  < 2e-16 ***
## d      1.10731    0.15429   7.177 1.06e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8816 on 1718 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (31 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85284, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.7205, p-value = 2.353e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 7 rows containing missing values (geom_point).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   2527     1959.3                               
## 2   2526     1953.0  1   6.279  8.1215 0.00441 ** 
## 3   2484     1815.2 42 137.796  4.4896 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 9211.166
## 2     2 9205.038
## 3     3 9021.180
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.71450    0.54278  -1.316   0.1882    
## phi    0.04659    0.01839   2.534   0.0113 *  
## alpha  0.68943    0.05997  11.496  < 2e-16 ***
## a      0.64584    0.13706   4.712 2.59e-06 ***
## b      2.02783    0.30420   6.666 3.23e-11 ***
## c     80.25839    4.76324  16.850  < 2e-16 ***
## d      1.46671    0.12238  11.985  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8548 on 2484 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (121 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88181, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.4317, p-value = 5.582e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 28 rows containing missing values (geom_point).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   1699     965.89                             
## 2   1698     964.53  1  1.359  2.3932  0.122    
## 3   1669     879.04 29 85.494  5.5974 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7044.476
## 2     2 7044.076
## 3     3 6861.430
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.29122    0.77522  -0.376    0.707    
## phi    0.01886    0.02134   0.884    0.377    
## alpha  0.74650    0.06311  11.829  < 2e-16 ***
## a      0.84169    0.19535   4.309 1.74e-05 ***
## b      3.16485    0.59477   5.321 1.17e-07 ***
## c     52.53802    1.86680  28.143  < 2e-16 ***
## d      1.28591    0.08224  15.636  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7257 on 1669 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (77 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9217, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.5838, p-value = 4.566e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 14 rows containing missing values (geom_point).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Error in nls(fg1_MBg5, data = G_M334, start = c(ge = ge.start, a = a.start,  : 
##   Convergence failure: singular convergence (7)
## Error in nls(fg2_MBg5, data = G_M334, start = c(ge = ge.start, phi = phi.start,  : 
##   Convergence failure: iteration limit reached without convergence (10)
##   model      AIC
## 1     1       NA
## 2     2       NA
## 3     3 1307.702
## 
## Formula: G_MassBal_g5_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * 
##     (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * 
##     exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -3.63950    0.11263 -32.312  < 2e-16 ***
## phi    0.07200    0.02858   2.520 0.012193 *  
## alpha  0.68326    0.17569   3.889 0.000121 ***
## a      0.00000   56.36679   0.000 1.000000    
## b      4.67839   56.15257   0.083 0.933648    
## c     72.87014   25.79751   2.825 0.005005 ** 
## d      2.07779   14.63256   0.142 0.887164    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.4335 on 348 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (104 observations deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89611, p-value = 7.794e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.1791, p-value = 2.926e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3
212 Laurentian Mixed Forest 3
221 Eastern Broadleaf Forest 3
222 Midwest Broadleaf Forest 3
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3
232 Outer Coastal Plain Mixed Forest 3
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) 3
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest 3
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 2
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 3
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6877 2876 1.1358026 0.0718957 0.6101767 1.6614285 0.0142553 0.0000297 0.0035740 0.0249365 0.1831049 0.0015752 0.1053031 0.2609067 0.5405335 0.2103135 0.8707534 2.2063530 1.8283002 2.584406 52.44769 50.51509 54.38029 1.3183883 1.1485289 1.4882478
212 Laurentian Mixed Forest east 22715 9499 1.5678652 0.0499832 1.1296495 2.0060809 0.0250033 0.0000138 0.0177240 0.0322825 0.1841802 0.0007896 0.1291003 0.2392600 0.3562359 0.3128153 0.3996564 1.7772086 1.6565075 1.897910 41.46903 40.63172 42.30635 1.2381687 1.1945906 1.2817468
221 Eastern Broadleaf Forest east 7333 3571 -0.7478866 0.0196814 -1.0228966 -0.4728765 0.0198284 0.0000310 0.0089093 0.0307475 0.5447131 0.0017315 0.4631426 0.6262836 1.2513411 0.3323367 2.1703456 3.3711544 2.4391496 4.303159 46.48696 42.66900 50.30493 1.7680525 1.3562954 2.1798095
222 Midwest Broadleaf Forest east 5845 2589 -0.1313922 0.0639750 -0.6272556 0.3644713 0.0301678 0.0001022 0.0103500 0.0499856 0.4047612 0.0026436 0.3039623 0.5055600 0.7833034 0.5568561 1.0097507 2.6926746 2.3794957 3.005854 52.54274 49.36696 55.71853 1.3455341 1.1993226 1.4917455
223 Central Interior Broadleaf Forest east 10010 3864 -0.4673151 0.0209933 -0.7513347 -0.1832956 0.0000000 0.0000424 -0.0127589 0.0127589 0.3751680 0.0018816 0.2901389 0.4601971 1.2758269 0.6062395 1.9454142 2.5734109 1.8995209 3.247301 36.25743 33.92007 38.59478 1.4802542 1.1665750 1.7939333
231 Southeastern Mixed Forest east 13517 6193 2.0662376 0.0558116 1.6031638 2.5293115 0.0137735 0.0000224 0.0045038 0.0230432 0.6016415 0.0004961 0.5579835 0.6452995 0.6826103 0.5023169 0.8629036 3.5726505 3.2793706 3.865930 24.57605 23.91630 25.23579 1.5400092 1.4524170 1.6276014
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.6294507 0.0586842 1.1546096 2.1042919 0.0133276 0.0000267 0.0032037 0.0234516 0.5884011 0.0005190 0.5437450 0.6330572 0.5453645 0.3224131 0.7683159 3.5037118 3.1728598 3.834564 23.68518 22.93704 24.43331 1.6248092 1.5155611 1.7340574
234 Lower Mississippi Riverine Forest east 1388 778 1.6344890 1.6236070 -0.8652143 4.1341923 0.0003623 0.0005627 -0.0461744 0.0468989 0.7133628 0.0083146 0.5344799 0.8922456 1.7316791 -1.3883318 4.8516900 2.1144852 -1.0164079 5.245378 26.02657 18.85077 33.20237 1.5411483 -0.2844287 3.3667253
242 Pacific Lowland Mixed Forest pacific 83 83 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2295 906 0.7993703 0.3143340 -0.3002443 1.8989849 0.0127219 0.0001539 -0.0116103 0.0370541 0.0546507 0.0119575 -0.1598183 0.2691198 1.6245155 0.9240594 2.3249716 0.9798006 0.2967198 1.662881 40.36397 33.41277 47.31517 1.2148696 0.4880126 1.9417266
255 Prairie Parkland (Subtropical) east 717 319 0.6385901 1.5778126 -1.8278227 3.1050028 0.0896379 0.0011187 0.0239636 0.1553122 0.2290813 0.0498229 -0.2091997 0.6673623 1.0181837 0.4121230 1.6242444 1.9876145 0.9011419 3.074087 23.95708 19.29381 28.62035 0.8519050 0.4936622 1.2101478
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 2.0206783 0.1149621 1.3560124 2.6853443 0.0145752 0.0000243 0.0049025 0.0242479 0.1912260 0.0012495 0.1219334 0.2605185 0.2789192 0.0661806 0.4916579 1.9803640 1.6926687 2.268059 58.30342 55.93177 60.67507 1.3885158 1.2446280 1.5324036
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 0.5858733 0.0453673 0.1683474 1.0033992 0.0000000 0.0000409 -0.0125325 0.0125325 0.5815929 0.0031381 0.4717815 0.6914044 1.3424552 0.4358128 2.2490975 2.7846037 1.8808488 3.688359 33.90742 31.34900 36.46583 1.5504517 1.1467369 1.9541665
M223 Ozark Broadleaf Forest Meadow east 896 349 2.4737170 2.0906244 -0.3640874 5.3115215 0.0000000 0.0006511 -0.0500792 0.0500792 0.3960003 0.0257320 0.0811669 0.7108337 1.5488202 0.9133961 2.1842444 1.2685985 0.5576736 1.979523 29.68437 25.76196 33.60678 0.4998388 0.2952899 0.7043878
M231 Ouachita Mixed Forest east 1006 495 2.3427611 2.3890459 -0.6903881 5.3759103 0.0433228 0.0006285 -0.0058748 0.0925204 0.4495133 0.0133907 0.2224309 0.6765957 0.0000000 -10.8412117 10.8412117 2.0190667 -8.7991435 12.837277 26.31121 16.83919 35.78324 2.7376676 -6.0092775 11.4846126
M242 Cascade Mixed Forest pacific 3224 3207 -1.7507253 0.0783782 -2.2996514 -1.2017992 0.0395038 0.0003333 0.0037079 0.0752997 0.9539747 0.0056843 0.8061470 1.1018024 6.7169542 5.4606953 7.9732131 5.3157755 3.3622132 7.269338 34.74904 31.65991 37.83816 0.3275765 0.2233085 0.4318446
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -2.0083777 0.0936842 -2.6087169 -1.4080385 0.2202471 0.0002644 0.1883558 0.2521384 0.5183634 0.0135602 0.2899633 0.7467635 0.0000000 -18.6036428 18.6036428 9.2128439 -9.3333568 27.759045 47.43124 30.55390 64.30858 2.7855897 -0.9876905 6.5588698
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.1537882 0.1652590 -2.9532493 -1.3543271 0.0523140 0.0007192 -0.0004255 0.1050534 NA NA NA NA 0.0000000 -10.2665361 10.2665361 3.3942993 -7.0093791 13.797978 55.12209 23.50524 86.73894 1.9640393 -2.3621063 6.2901849
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 -0.5558620 0.4482148 -1.8689603 0.7572364 0.0726215 0.0002397 0.0422529 0.1029901 0.5160623 0.0039592 0.3926500 0.6394745 0.7741773 0.4061840 1.1421706 1.2274666 0.7583769 1.696556 65.00451 56.60712 73.40191 1.1073097 0.8046946 1.4099248
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -0.7144995 0.2946088 -1.7788449 0.3498459 0.0465865 0.0003380 0.0105346 0.0826385 0.6894272 0.0035962 0.5718338 0.8070206 0.6458423 0.3770725 0.9146120 2.0278279 1.4313095 2.624346 80.25839 70.91806 89.59871 1.4667143 1.2267428 1.7066859
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 -0.2912166 0.6009678 -1.8117248 1.2292916 0.0188591 0.0004555 -0.0230006 0.0607188 0.7465015 0.0039829 0.6227177 0.8702852 0.8416879 0.4585357 1.2248401 3.1648466 1.9982701 4.331423 52.53802 48.87651 56.19953 1.2859073 1.1245978 1.4472168
M334 Black Hills Coniferous Forest interior west 459 181 -3.6394992 0.0126865 -3.8610292 -3.4179693 0.0720006 0.0008165 0.0157986 0.1282026 0.6832624 0.0308657 0.3377219 1.0288030 0.0000000 -110.8624479 110.8624479 4.6783912 -105.7627115 115.119494 72.87014 22.13149 123.60879 2.0777924 -26.7015797 30.8571645
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 16 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.61164549            0.07927918    0.767032675      0.4562583
## 2       pacific -0.15958074            0.01820490   -0.123899140     -0.1952623
## 3          east  0.85394889            0.06631074    0.983917935      0.7239799
## 4 interior west -0.08272266            0.03945448   -0.005391883     -0.1600534

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  0.026675612            0.002162048    0.030913227
## 2       pacific  0.009057837            0.001130894    0.011274389
## 3          east  0.012199987            0.001429816    0.015002426
## 4 interior west  0.005417788            0.001162393    0.007696079
##   95 % CI, lower
## 1    0.022437998
## 2    0.006841284
## 3    0.009397549
## 4    0.003139497

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.45391179              0.011314723     0.47608865
## 2       pacific     0.06898713              0.005533544     0.07983288
## 3          east     0.31372619              0.009088688     0.33154002
## 4 interior west     0.07119846              0.003846895     0.07873838
##   95 % CI, lower
## 1     0.43173493
## 2     0.05814139
## 3     0.29591237
## 4     0.06365855

Analaysis 2: \(G_{TI-NoIngrow}\)

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   6869     3216.6                              
## 2   6868     3216.5  1   0.056  0.1204 0.7286    
## 3   6816     3000.9 52 215.657  9.4199 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24882.32
## 2     2 24884.20
## 3     3 24355.03
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.051904   0.287972   3.653 0.000261 ***
## phi    0.006179   0.005892   1.049 0.294374    
## alpha  0.836251   0.038662  21.630  < 2e-16 ***
## a      0.504459   0.045721  11.033  < 2e-16 ***
## b      1.844700   0.097873  18.848  < 2e-16 ***
## c     68.869770   1.253421  54.945  < 2e-16 ***
## d      0.974340   0.037853  25.740  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6635 on 6816 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (54 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  19351      23127                                  
## 2  19346      23042   5   84.74 14.2293  6.28e-14 ***
## 3  18857      21019 489 2023.12  3.7117 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 63998.00
## 2     2 63917.40
## 3     3 61608.95
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.083416   0.220332   4.917 8.85e-07 ***
## phi    0.036821   0.004243   8.679  < 2e-16 ***
## alpha  1.042066   0.026868  38.785  < 2e-16 ***
## a      0.301247   0.013973  21.559  < 2e-16 ***
## b      1.351310   0.048031  28.134  < 2e-16 ***
## c     61.261958   0.812407  75.408  < 2e-16 ***
## d      1.023659   0.020133  50.844  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.056 on 18857 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (3851 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 40 rows containing missing values (geom_point).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7319     3643.2                                
## 2   7318     3639.8  1   3.46  6.9571  0.008366 ** 
## 3   7254     3430.7 64 209.12  6.9091 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 31554.54
## 2     2 31549.58
## 3     3 30985.52
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.762389   0.148296  -5.141 2.80e-07 ***
## phi    0.015255   0.005847   2.609   0.0091 ** 
## alpha  0.846238   0.042069  20.116  < 2e-16 ***
## a      0.952663   0.185209   5.144 2.76e-07 ***
## b      3.045339   0.207132  14.702  < 2e-16 ***
## c     62.842867   2.659028  23.634  < 2e-16 ***
## d      1.503863   0.115430  13.028  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6877 on 7254 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (72 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df Sum Sq F value  Pr(>F)    
## 1   5044     4308.4                               
## 2   5043     4303.7   1   4.75   5.567 0.01834 *  
## 3   4823     3732.6 220 571.06   3.354 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19723.24
## 2     2 19719.67
## 3     3 18603.89
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.08175    0.28217   -0.29  0.77206    
## phi    0.02831    0.01093    2.59  0.00963 ** 
## alpha  0.99507    0.04935   20.16  < 2e-16 ***
## a      0.61151    0.05628   10.87  < 2e-16 ***
## b      2.30415    0.12387   18.60  < 2e-16 ***
## c     63.30978    1.66568   38.01  < 2e-16 ***
## d      1.05644    0.04900   21.56  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8797 on 4823 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1015 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 8 rows containing missing values (geom_point).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Error in nls(fg2_TI, data = G_223, start = c(ge = ge.start, a = a.start,  : 
##   parameters without starting value in 'data': phi
##   model      AIC
## 1     1 34828.86
## 2     2       NA
## 3     3 34003.35
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.803798   0.137371  -5.851 5.05e-09 ***
## phi    0.000000   0.007125   0.000        1    
## alpha  0.757366   0.044133  17.161  < 2e-16 ***
## a      0.853571   0.172881   4.937 8.07e-07 ***
## b      2.441732   0.182297  13.394  < 2e-16 ***
## c     50.681798   1.212794  41.789  < 2e-16 ***
## d      1.302611   0.090146  14.450  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8075 on 8729 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (1274 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  13446      12254                                  
## 2  13445      12246   1    7.41  8.1354  0.004348 ** 
## 3  13194      11030 251 1215.95  5.7947 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 66367.52
## 2     2 66361.38
## 3     3 64655.63
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.605908   0.253031   6.347 2.27e-10 ***
## phi    0.014040   0.005778   2.430   0.0151 *  
## alpha  0.944623   0.025460  37.102  < 2e-16 ***
## a      0.478924   0.031667  15.124  < 2e-16 ***
## b      3.166561   0.128340  24.673  < 2e-16 ***
## c     34.289511   0.518135  66.179  < 2e-16 ***
## d      1.275092   0.026627  47.887  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9143 on 13194 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (316 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 27 rows containing missing values (geom_point).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1  13504      15331                                  
## 2  13503      15316   1   15.08 13.2932 0.0002674 ***
## 3  13220      13788 283 1527.57  5.1754 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 65934.14
## 2     2 65922.84
## 3     3 64075.10
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.139737   0.245775   4.637 3.56e-06 ***
## phi    0.019881   0.006102   3.258  0.00112 ** 
## alpha  0.963979   0.024979  38.592  < 2e-16 ***
## a      0.411257   0.035530  11.575  < 2e-16 ***
## b      3.029624   0.129878  23.327  < 2e-16 ***
## c     32.680017   0.527000  62.011  < 2e-16 ***
## d      1.308955   0.029869  43.824  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.021 on 13220 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (402 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 57 rows containing missing values (geom_point).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1368     2135.0                                 
## 2   1367     2132.6  1   2.374  1.5216    0.2176    
## 3   1315     1973.4 52 159.159  2.0395 2.556e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7497.623
## 2     2 7498.096
## 3     3 7292.351
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.97717    0.58433  -1.672  0.09470 .  
## phi    0.09904    0.03555   2.786  0.00541 ** 
## alpha  0.91559    0.12085   7.576 6.68e-14 ***
## a      1.33887    0.29741   4.502 7.33e-06 ***
## b      3.66786    0.63036   5.819 7.44e-09 ***
## c     42.96174    3.79018  11.335  < 2e-16 ***
## d      1.10915    0.18070   6.138 1.10e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.225 on 1315 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (66 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits ### plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.85289, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.6124, p-value = 3.98e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq  Df  Sum Sq F value    Pr(>F)    
## 1   1888     1534.7                                  
## 2   1887     1533.9   1   0.786  0.9664    0.3257    
## 3   1772     1348.7 115 185.236  2.1163 2.841e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6937.884
## 2     2 6938.914
## 3     3 6461.892
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.991649   0.608307   1.630    0.103    
## phi    0.002689   0.012481   0.215    0.829    
## alpha  0.494173   0.103537   4.773 1.96e-06 ***
## a      0.750331   0.166810   4.498 7.30e-06 ***
## b      1.354466   0.204618   6.619 4.76e-11 ***
## c     55.232328   2.635890  20.954  < 2e-16 ***
## d      1.117919   0.139079   8.038 1.65e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8724 on 1772 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (516 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90525, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -10.713, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 9 rows containing missing values (geom_point).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    710     3128.3                              
## 2    709     3093.4  1 34.963  8.0136 0.004774 **
## 3    666     2994.5 43 98.892  0.5115 0.996202   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3570.774
## 2     2 3564.738
## 3     3 3509.035
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.89797    4.96252   0.785  0.43245    
## phi    0.16636    0.05922   2.809  0.00511 ** 
## alpha  0.22739    0.37758   0.602  0.54723    
## a      0.15024    0.09137   1.644  0.10061    
## b      1.03213    0.61042   1.691  0.09133 .  
## c     29.91856    2.76638  10.815  < 2e-16 ***
## d      0.87522    0.15129   5.785 1.12e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.12 on 666 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (44 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9002, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.2453, p-value = 1.561e-07
## alternative hypothesis: two.sided

predict and plot

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

332 - Great Plains Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   6765     3120.3                                 
## 2   6764     3111.3  1   9.075  19.729 9.066e-06 ***
## 3   6740     2905.7 24 205.555  19.867 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23241.99
## 2     2 23224.27
## 3     3 22758.44
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.530710   0.344829   4.439 9.18e-06 ***
## phi    0.021453   0.005869   3.655 0.000259 ***
## alpha  0.822003   0.035969  22.853  < 2e-16 ***
## a      0.256549   0.035128   7.303 3.13e-13 ***
## b      1.715201   0.103495  16.573  < 2e-16 ***
## c     74.557987   1.725691  43.205  < 2e-16 ***
## d      1.085542   0.039201  27.692  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.6566 on 6740 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (25 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   8308     4928.4                             
## 2   8307     4928.4  1   0.00  0.0000      1    
## 3   8252     4767.3 55 161.05  5.0684 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 37694.53
## 2     2 37696.53
## 3     3 37287.40
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     1.173351   0.275774   4.255 2.12e-05 ***
## phi    0.000000   0.006795   0.000        1    
## alpha  0.905989   0.057344  15.799  < 2e-16 ***
## a      0.672806   0.162564   4.139 3.53e-05 ***
## b      2.343638   0.191092  12.264  < 2e-16 ***
## c     47.556263   1.190460  39.948  < 2e-16 ***
## d      1.374358   0.091086  15.089  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7601 on 8252 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (56 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    890     702.27                                
## 2    889     702.27  1  0.000  0.0000 0.9999882    
## 3    882     680.17  7 22.094  4.0928 0.0001961 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3537.006
## 2     2 3539.006
## 3     3 3505.262
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     4.23213    2.58117   1.640  0.10144    
## phi    0.00000    0.02955   0.000  1.00000    
## alpha  1.00897    0.17368   5.809 8.76e-09 ***
## a      0.00000    0.25140   0.000  1.00000    
## b      1.31904    0.44853   2.941  0.00336 ** 
## c     42.48170    2.77050  15.334  < 2e-16 ***
## d      1.27733    0.25380   5.033 5.86e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8782 on 882 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96657, p-value = 2.1e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.1895, p-value = 0.001425
## alternative hypothesis: two.sided

predict and plot

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1000     894.75                                
## 2    999     888.75  1  5.991  6.7337 0.0095995 ** 
## 3    986     853.58 13 35.172  3.1252 0.0001365 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4182.168
## 2     2 4177.416
## 3     3 4124.944
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.39959    2.57363   1.321   0.1868    
## phi    0.05633    0.03145   1.791   0.0736 .  
## alpha  0.82574    0.13610   6.067 1.85e-09 ***
## a      0.00000    0.33600   0.000   1.0000    
## b      1.36576    0.53765   2.540   0.0112 *  
## c     46.69611    5.96158   7.833 1.23e-14 ***
## d      1.75435    0.43638   4.020 6.26e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9304 on 986 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93331, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.7781, p-value = 1.218e-11
## alternative hypothesis: two.sided

predict and plot

plotting 2

M242 - Cascade Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   3140     2906.2                             
## 2   3139     2906.2  1   0.00   0.000      1    
## 3   3126     2741.5 13 164.71  14.446 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 16154.59
## 2     2 16156.59
## 3     3 15944.25
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -1.69012    0.28448  -5.941 3.14e-09 ***
## phi    0.01996    0.01842   1.084  0.27855    
## alpha  1.07660    0.07203  14.947  < 2e-16 ***
## a      0.00000    2.13763   0.000  1.00000    
## b      6.23192    2.18152   2.857  0.00431 ** 
## c     94.67459    6.83750  13.846  < 2e-16 ***
## d      2.47547    0.59713   4.146 3.48e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9365 on 3126 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (91 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.9091, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -13.884, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 17 rows containing missing values (geom_point).

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   1681     1785.5                                
## 2   1680     1696.7  1 88.808 87.9362 < 2.2e-16 ***
## 3   1667     1639.5 13 57.180  4.4723 1.565e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 7935.257
## 2     2 7851.239
## 3     3 7752.077
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.00185    0.29365  -6.817 1.29e-11 ***
## phi    0.19755    0.01621  12.190  < 2e-16 ***
## alpha  0.85077    0.10568   8.051 1.55e-15 ***
## a      2.93799    2.07549   1.416  0.15709    
## b      4.95009    2.04338   2.422  0.01552 *  
## c     49.61092    8.44463   5.875 5.10e-09 ***
## d      1.77705    0.67708   2.625  0.00875 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9917 on 1667 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (303 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92265, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.2743, p-value = 0.02295
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 10 rows containing missing values (geom_point).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    360     195.96                              
## 2    359     192.66  1 3.2997  6.1486 0.013610 * 
## 3    358     187.44  1 5.2135  9.9573 0.001738 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 988.1197
## 2     2 983.9212
## 3     3 975.9079
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -2.50496    0.32713  -7.657 1.79e-13 ***
## phi    0.05300    0.03034   1.747 0.081532 .  
## alpha  0.56839    0.16252   3.497 0.000529 ***
## a      0.00000    2.13594   0.000 1.000000    
## b      3.59723    2.24022   1.606 0.109210    
## c     67.83177   13.21943   5.131 4.73e-07 ***
## d      1.66097    0.89415   1.858 0.064047 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7236 on 358 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (2 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93652, p-value = 2.287e-11
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.0261, p-value = 0.04275
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   1736     1676.4                                 
## 2   1735     1662.8  1  13.595 14.1858 0.0001711 ***
## 3   1718     1540.4 17 122.428  8.0321 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4364.968
## 2     2 4352.791
## 3     3 4221.416
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.62425    1.16195   0.537    0.591    
## phi    0.08324    0.01580   5.270 1.54e-07 ***
## alpha  0.76591    0.05979  12.810  < 2e-16 ***
## a      0.48403    0.11880   4.074 4.82e-05 ***
## b      0.76035    0.17728   4.289 1.89e-05 ***
## c     82.23818    4.81492  17.080  < 2e-16 ***
## d      0.89016    0.10097   8.816  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9469 on 1718 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (31 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.88198, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.2914, p-value = 1.775e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 11 rows containing missing values (geom_point).

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2527     2344.7                                
## 2   2526     2335.0  1   9.70 10.4936  0.001213 ** 
## 3   2484     2108.9 42 226.01  6.3381 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8552.063
## 2     2 8543.566
## 3     3 8318.048
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.83807    0.50931  -1.646  0.09999 .  
## phi    0.05563    0.01810   3.074  0.00214 ** 
## alpha  0.95007    0.05611  16.933  < 2e-16 ***
## a      0.51222    0.08760   5.847 5.66e-09 ***
## b      2.11381    0.29325   7.208 7.48e-13 ***
## c     89.98718    4.03032  22.328  < 2e-16 ***
## d      1.24548    0.07416  16.794  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9214 on 2484 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (121 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.86768, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -4.7153, p-value = 2.413e-06
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 22 rows containing missing values (geom_point).

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)    
## 1   1699     1220.6                             
## 2   1698     1220.3  1   0.32  0.4458 0.5044    
## 3   1669     1059.1 29 161.22  8.7611 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 6534.582
## 2     2 6536.134
## 3     3 6297.177
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.844464   1.264188   0.668    0.504    
## phi    0.008227   0.022153   0.371    0.710    
## alpha  0.977482   0.061116  15.994  < 2e-16 ***
## a      0.465264   0.114098   4.078 4.76e-05 ***
## b      2.367204   0.556112   4.257 2.19e-05 ***
## c     63.959874   1.887481  33.886  < 2e-16 ***
## d      1.082996   0.046847  23.118  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.7966 on 1669 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (77 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91308, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.8994, p-value = 3.647e-09
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 15 rows containing missing values (geom_point).

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 2: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## Model 3: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    357     618.39                            
## 2    356     618.17  1  0.215  0.1239 0.72507  
## 3    348     584.57  8 33.604  2.5006 0.01188 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 1072.454
## 2     2 1074.328
## 3     3 1044.319
## 
## Formula: G_obs_TreeInc_NoIngrow_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * 
##     ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * 
##     (a + b * exp(-((log(STDAGE_t1/c))/d)^2))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -1.19519    1.41779  -0.843    0.400    
## phi     0.00000    0.04476   0.000    1.000    
## alpha   0.68660    0.16773   4.093 5.29e-05 ***
## a       0.00000    7.85050   0.000    1.000    
## b       1.40538    7.82290   0.180    0.858    
## c     125.20338  121.81266   1.028    0.305    
## d       2.50306    9.55036   0.262    0.793    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.296 on 348 degrees of freedom
## 
## Algorithm "port", convergence message: relative convergence (4)
##   (104 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96219, p-value = 6.081e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.952, p-value = 7.749e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3
212 Laurentian Mixed Forest 3
221 Eastern Broadleaf Forest 3
222 Midwest Broadleaf Forest 3
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3
232 Outer Coastal Plain Mixed Forest 3
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) 3
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe NA
332 Great Plains Steppe NA
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest 3
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow 3
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow 3
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow 3
M334 Black Hills Coniferous Forest 3
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 a a.2.5 a.97.5 b b.2.5 b.97.5 c c.2.5 c.97.5 d d.2.5 d.97.5
211 Northeastern Mixed Forest east 6877 2876 1.0519043 0.0829277 0.4873898 1.6164188 0.0061791 0.0000347 -0.0053718 0.0177299 0.8362509 0.0014948 0.7604605 0.9120413 0.5044588 0.4148313 0.5940863 1.8447001 1.6528388 2.036561 68.86977 66.41267 71.32687 0.9743399 0.9001357 1.048544
212 Laurentian Mixed Forest east 22715 9499 1.0834155 0.0485461 0.6515456 1.5152854 0.0368214 0.0000180 0.0285051 0.0451377 1.0420658 0.0007219 0.9894021 1.0947295 0.3012473 0.2738593 0.3286353 1.3513096 1.2571637 1.445456 61.26196 59.66957 62.85435 1.0236589 0.9841957 1.063122
221 Eastern Broadleaf Forest east 7333 3571 -0.7623894 0.0219916 -1.0530923 -0.4716864 0.0152547 0.0000342 0.0037924 0.0267170 0.8462383 0.0017698 0.7637711 0.9287054 0.9526626 0.5895988 1.3157264 3.0453393 2.6393007 3.451378 62.84287 57.63040 68.05534 1.5038627 1.2775867 1.730139
222 Midwest Broadleaf Forest east 5845 2589 -0.0817463 0.0796215 -0.6349338 0.4714411 0.0283120 0.0001195 0.0068811 0.0497428 0.9950652 0.0024354 0.8983177 1.0918127 0.6115125 0.5011758 0.7218492 2.3041529 2.0613073 2.546998 63.30978 60.04427 66.57528 1.0564370 0.9603756 1.152498
223 Central Interior Broadleaf Forest east 10010 3864 -0.8037980 0.0188709 -1.0730783 -0.5345176 0.0000000 0.0000508 -0.0139675 0.0139675 0.7573656 0.0019477 0.6708546 0.8438766 0.8535710 0.5146840 1.1924580 2.4417317 2.0843858 2.799078 50.68180 48.30444 53.05916 1.3026110 1.1259027 1.479319
231 Southeastern Mixed Forest east 13517 6193 1.6059080 0.0640245 1.1099317 2.1018843 0.0140402 0.0000334 0.0027140 0.0253664 0.9446226 0.0006482 0.8947175 0.9945277 0.4789238 0.4168518 0.5409959 3.1665610 2.9149967 3.418125 34.28951 33.27389 35.30513 1.2750921 1.2228990 1.327285
232 Outer Coastal Plain Mixed Forest east 13629 6626 1.1397371 0.0604051 0.6579838 1.6214904 0.0198812 0.0000372 0.0079208 0.0318415 0.9639789 0.0006240 0.9150165 1.0129413 0.4112567 0.3416138 0.4808997 3.0296240 2.7750453 3.284203 32.68002 31.64702 33.71301 1.3089545 1.2504079 1.367501
234 Lower Mississippi Riverine Forest east 1388 778 -0.9771746 0.3414432 -2.1234982 0.1691490 0.0990410 0.0012636 0.0293062 0.1687758 0.9155910 0.0146047 0.6785114 1.1526707 1.3388700 0.7554249 1.9223150 3.6678550 2.4312332 4.904477 42.96174 35.52629 50.39719 1.1091545 0.7546573 1.463652
242 Pacific Lowland Mixed Forest pacific 83 83 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 2295 906 0.9916487 0.3700369 -0.2014252 2.1847225 0.0026890 0.0001558 -0.0217893 0.0271673 0.4941728 0.0107199 0.2911053 0.6972402 0.7503314 0.4231671 1.0774957 1.3544657 0.9531469 1.755785 55.23233 50.06255 60.40211 1.1179190 0.8451422 1.390696
255 Prairie Parkland (Subtropical) east 717 319 3.8979749 24.6266523 -5.8461030 13.6420527 0.1663586 0.0035071 0.0500771 0.2826400 0.2273884 0.1425695 -0.5140094 0.9687862 0.1502383 -0.0291782 0.3296547 1.0321300 -0.1664488 2.230709 29.91856 24.48669 35.35043 0.8752194 0.5781515 1.172287
261 California Coastal Chaparral Forest and Shrub pacific 25 25 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 163 161 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 218 218 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 4 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 9 9 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 3 3 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 331 255 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
332 Great Plains Steppe interior west 232 128 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
341 Intermountain Semi-Desert and Desert interior west 66 64 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 124 123 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 96 63 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 6772 3006 1.5307098 0.1189068 0.8547368 2.2066828 0.0214535 0.0000344 0.0099480 0.0329589 0.8220032 0.0012938 0.7514927 0.8925136 0.2565489 0.1876879 0.3254099 1.7152006 1.5123176 1.918084 74.55799 71.17509 77.94089 1.0855416 1.0086953 1.162388
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 8315 3810 1.1733507 0.0760512 0.6327646 1.7139367 0.0000000 0.0000462 -0.0133202 0.0133202 0.9059893 0.0032884 0.7935800 1.0183986 0.6728062 0.3541398 0.9914726 2.3436378 1.9690490 2.718227 47.55626 45.22266 49.88986 1.3743578 1.1958064 1.552909
M223 Ozark Broadleaf Forest Meadow east 896 349 4.2321262 6.6624426 -0.8338274 9.2980798 0.0000000 0.0008730 -0.0579882 0.0579882 1.0089721 0.0301655 0.6680934 1.3498508 0.0000000 -0.4934201 0.4934201 1.3190443 0.4387343 2.199354 42.48170 37.04414 47.91925 1.2773344 0.7792114 1.775457
M231 Ouachita Mixed Forest east 1006 495 3.3995885 6.6235564 -1.6508274 8.4500044 0.0563340 0.0009892 -0.0053865 0.1180546 0.8257426 0.0185220 0.5586721 1.0928130 0.0000000 -0.6593637 0.6593637 1.3657568 0.3106896 2.420824 46.69611 34.99727 58.39496 1.7543539 0.8980146 2.610693
M242 Cascade Mixed Forest pacific 3224 3207 -1.6901211 0.0809302 -2.2479122 -1.1323300 0.0199631 0.0003393 -0.0161533 0.0560795 1.0765993 0.0051881 0.9353713 1.2178273 0.0000000 -4.1913051 4.1913051 6.2319169 1.9545535 10.509280 94.67459 81.26815 108.08103 2.4754690 1.3046649 3.646273
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 1977 1807 -2.0018515 0.0862282 -2.5778061 -1.4258969 0.1975535 0.0002627 0.1657656 0.2293413 0.8507713 0.0111676 0.6434979 1.0580446 2.9379945 -1.1328545 7.0088436 4.9500868 0.9422226 8.957951 49.61092 33.04772 66.17411 1.7770464 0.4490395 3.105053
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 30 26 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 367 367 -2.5049581 0.1070130 -3.1482929 -1.8616232 0.0530004 0.0009206 -0.0066699 0.1126706 0.5683921 0.0264132 0.2487753 0.8880088 0.0000000 -4.2005688 4.2005688 3.5972300 -0.8084094 8.002869 67.83177 41.83426 93.82927 1.6609659 -0.0974751 3.419407
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 1756 1756 0.6242463 1.3501290 -1.6547405 2.9032331 0.0832436 0.0002495 0.0522604 0.1142268 0.7659065 0.0035748 0.6486378 0.8831753 0.4840268 0.2510241 0.7170294 0.7603507 0.4126472 1.108054 82.23818 72.79446 91.68190 0.8901647 0.6921241 1.088205
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 2612 2602 -0.8380746 0.2593952 -1.8367876 0.1606385 0.0556339 0.0003276 0.0201397 0.0911282 0.9500686 0.0031481 0.8400461 1.0600911 0.5122166 0.3404392 0.6839940 2.1138072 1.5387742 2.688840 89.98718 82.08404 97.89032 1.2454840 1.1000550 1.390913
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 1753 1742 0.8444638 1.5981707 -1.6350968 3.3240245 0.0082270 0.0004908 -0.0352237 0.0516778 0.9774818 0.0037352 0.8576093 1.0973544 0.4652640 0.2414740 0.6890540 2.3672043 1.2764546 3.457954 63.95987 60.25779 67.66195 1.0829957 0.9911111 1.174880
M334 Black Hills Coniferous Forest interior west 459 181 -1.1951946 2.0101417 -3.9837191 1.5933299 0.0000000 0.0020037 -0.0880392 0.0880392 0.6865993 0.0281345 0.3567005 1.0164981 0.0000000 -15.4403982 15.4403982 1.4053800 -13.9807277 16.791488 125.20338 -114.37826 364.78503 2.5030610 -16.2806247 21.286747
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 220 220 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot a coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot b coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

plot c coefficient

## Warning: Removed 1 rows containing missing values (geom_hline).
## Warning: Removed 19 rows containing missing values (geom_point).

plot d coefficient

## Warning: Removed 15 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region weighted.ge weighted.ge.std_Error 95 % CI, upper 95 % CI, lower
## 1     entire US  0.49375055            0.09590657     0.68172742      0.3057737
## 2       pacific -0.15602182            0.01822046    -0.12030973     -0.1917339
## 3          east  0.66270439            0.07505051     0.80980338      0.5156054
## 4 interior west -0.01293202            0.05686392     0.09852127     -0.1243853

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US  0.029083247            0.002342738    0.033675014
## 2       pacific  0.007268032            0.001138258    0.009499018
## 3          east  0.016209381            0.001673911    0.019490246
## 4 interior west  0.005605834            0.001179328    0.007917317
##   95 % CI, lower
## 1    0.024491479
## 2    0.005037046
## 3    0.012928516
## 4    0.003294351

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US     0.89468262              0.011392574     0.91701207
## 2       pacific     0.08614584              0.005174041     0.09628696
## 3          east     0.70749824              0.009416443     0.72595447
## 4 interior west     0.10103855              0.003788224     0.10846347
##   95 % CI, lower
## 1     0.87235318
## 2     0.07600472
## 3     0.68904201
## 4     0.09361363